A multigrid solver for incompressible Navier-Stokes on non-staggered grids

David Sidilkover

Courant Institute, New York University, New York, NY 10012, USA

Uri M. Ascher

Department of Computer Science, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada


Abstract

The goal of this work is to develop an efficient multigrid solver for the steady-state incompressible Navier-Stokes equations on non-staggered grids. The pressure Poisson equation (PPE) is used instead of the continuity equation in order to avoid odd-even pressure instability. The differential order of the resulting system of equations is higher than that of the original system, so additional boundary conditions are needed. For this, Neumann-type boundary conditions for the pressure can be derived from the given boundary conditions (sufficient for the original formulation) using the momentum and continuity equations.

The main achievements of this work are:

The resulting fast solver is capable of producing second order accurate solutions for the entire range of Reynolds number.